Quenching of individual metastable states of antiprotonic helium ((p) over bar He+) in collisions with H-2 and D-2 in gas phase was studied using a laser-resonance method at CERN's Antiproton Decelerator. The temperature dependence of the quenching cross-sections of the (p) over bar He+ states (n, l) = (37, 34), (38, 35), and (38, 37) in the reactions [(p) over bar He+]((n,l)) + H-2 and [(p) over bar He+]((n,l)) + D-2 was investigated in the temperature range of 25-300 K. Significant quantum tunnelling effects were revealed at low temperatures and (n, l)-dependent reaction barriers were deduced, in good agreement with recent theoretical calculations. (C) 2003 Elsevier B.V. All rights reserved.